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mathematical geology
Theorems in pure mathematics can be proved right but the models used in applied mathematics, natural and social science, as well as in engineering, can at most be “not yet proved wrong”
Horatio Scott Carslaw and the origins of the well function and line source heat function
William Thomson – father of thermogeology
Abstract This book questions a basic assumption of the scientific method – that new theories or experimental results are communicated effectively by traditional methods (e.g., presentations at professional meetings or publication in a peer-reviewed journal) – and suggests that the scientific method needs to be applied to the scientific method itself to find out if other styles of communication might work better. In a highly entertaining format, the book uses the enormously popular fictional characters created by Sir Arthur Conan Doyle to unravel and explain the historical underpinnings of remote sensing. The extended appendices guarantee that all of the science of remote sensing is included in this book of “scientific fiction.” The story covers more than 2000 years, beginning with Pythagoras in ancient Greece and ending with Einstein’s first article on relativity in 1905. Light-years beyond a traditional science textbook, this detective story set in 1905 will teach students of all ages about the exciting journey of scientific discovery.
The role of integration and abstraction in complex systems thinking across multiple contexts
The science of subjectivity
Tools to aid the selection of ideal attribute parameter values
The Use and Misuse of Logic Trees in Probabilistic Seismic Hazard Analysis
A major objective of science is to provide a fundamental understanding of natural phenomena. In “the old kind of science,” this was done primarily by using partial differential equations. Boundary and initial value conditions were specified and solutions were obtained either analytically or numerically. However, many phenomena in geology are complex and statistical in nature and thus require alternative approaches. But the observed statistical distributions often are not Gaussian (normal) or lognormal, instead they are power laws. A power-law (fractal) distribution is a direct consequence of scale invariance, but it is now recognized to also be associated with self-organized complexity. Relatively simple cellular automata (CA) models provide explanations for a range of complex geological observations. The “sand-pile” model of Bak—the context for “self-organized criticality”—has been applied to landslides and turbidite deposits. The “forest-fire” model provides an explanation for the frequency-magnitude statistics of actual forest and wild fires. The slider-block model reproduces the Guttenberg-Richter frequency-magnitude scaling for earthquakes. Many of the patterns generated by the CA approach can be recognized in geological contexts. The use of CA models to provide an understanding of a wide range of natural phenomena has been popularized in Stephen Wolfram's bestselling book A New Kind of Science (2002) . Since CA models are basically computer games, they are accepted enthusiastically by many students who find other approaches to the quantification of geological problems both difficult and boring.
A statistical approach to estimate the 3D size distribution of spheres from 2D size distributions
Stability Analysis of Finite-Difference Approximations of Elastic Wave Equations
High radiogenic heat–producing granites and metamorphism—An example from the western Mount Isa inlier, Australia: Comment and Reply: REPLY
The Channeled Scabland: Back to Bretz?: Comment and Reply: REPLY
Environmental aqueous geochemistry of actinides
Abstract “This reference manual is designed to enable more geophysicists to appreciate static corrections, especially their limitations, their relationship with near-surface geology, and their impact on the quality of final interpreted sections. The book is addressed to those involved in data acquisition (datum static corrections), data processing (datum static and residual static corrections), and interpretation (the impact that unresolved static corrections, especially the long-wavelength or low-spatial-frequency component, have on interpretation of the final section). Simple explanations of the underlying principles are included in an attempt to remove some of the mystique of static corrections. The principles involved are illustrated with simple models, supplemented with many data examples. This book details differences in approaches that must be considered among 2D, 3D, and crooked-line recordings as well as between P-wave and S-wave surveys. Static corrections are shown to be a simplified yet practical approach to modeling the effects of the near surface where a more correct wavefield or raypath-modeled method might not be undertaken efficiently. Chapters cover near-surface topography and geology; computation of datum static corrections; uphole surveys; refraction surveys; static corrections limitations and effect on seismic data processes; residual static corrections; and interpretation aspects. An extensive index and a large list of references are included.”
Mathematics in the daily life of a geophysicist
A numerical approach for the formation of chlorite and sulphide-bearing greisen; a study based on the Navalcubilla System (Spanish Central System)
Transport properties and diagenesis in sedimentary rocks: The role of micro-scale geometry
Abstract The intention of these notes is to provide sedimentary geologists with an introduction to the new techniques for analyzing experimental and observational data provided by the rapid development of those disciplines generally known as Fractals and Nonlinear Dynamics (chaos theory). A general introduction to a minimum of theory is given, but most of the space is devoted to show how these ideas are useful for interpreting sedimentary data. The main applications are likely to be time series or spatial profiles or two-dimensional maps or images. Sedimentary geologists deal every day with actual time series, such as measurements of current velocity or suspended concentration at a station, or with virtual time series, such as stratigraphic sections, well logs, or topographic profiles yet few geologists know much about the new numerical techniques available to analyze such data.